Question

A mathematics teacher wanted to see the correlation between test

scores and homework. The homework grade (x) and test grade (y) are
given in the accompanying table. Write the linear regression equation
that represents this set of data, rounding all coefficients to the nearest
hundredth. Using this equation, find the projected test grade, to the
nearest integer, for a student with a homework grade of 61.
Homework Grade (x) 72 53 90 77 82 74 78 74 83Test Grade (y)
75 39 81 70 83 78 75 70 85

Answer 1

54

Explanation:

You want the approximate test grade of a student with a homework grade of 61, using a linear regression equation for the given homework and test scores.

Regression

The linear regression equation can be found using any of a number of calculators, apps, or spreadsheets. The attachment shows the equation is approximately ...

y ≈ 1.22x -20.01

For a homework score of 61, the expected test grade is ...

y = 1.22(61) -20.01

y ≈ 54

The student's projected test grade is 54.

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Additional comment

If the regression coefficients are used to their full precision, the projected test score is about 54.6, which rounds to 55.

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